Impact Factor: 0.5

Published since March 1, 2001

Advances in Geometry

ISSN: 1615-7168

Managing Editors: Theo Grundhöfer, Michael Joswig

Editorial Board: John Bamberg, Eiichi Bannai, Renzo Cavalieri, Izzet Coskun, Hans Cuypers, Patrick Eberlein, Graziano Gentili, Martin Henk, Milena Hering, William M. Kantor, Gabor Korchmaros, Alexander Kreuzer, Jeffrey C. Lagarias, Thomas Leistner, Rainer Löwen, Kaoru Ono, Daniel Plaumann, Francisco Santos, Steven H. Weintraub, Richard Weiss

About this journal

Objective
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.

Topics

Finite geometry
Incidence geometry
Tits buildings
Combinatorial aspects of geometry and geometric combinatorics
Geometric group theory
Geometric aspects of Lie groups and of algebraic groups
Algebraic geometry
Topological geometry
Differential geometry
Convex sets and polytopes
Discrete geometry

Article formats
Research articles

Submit Article

Your Benefits

Your benefits:

Leading journal in the field of geometry
Rigorous and thorough peer-review
Ahead of print online publication
Covered by major Abstracting and Indexing services

History

The journal was founded in 2001.

Other publications in the field

Abstracting and Indexing

Advances in Geometry is covered by the following services:

Baidu Scholar
Cabells Journalytics
CNKI Scholar (China National Knowledge Infrastructure)
CNPIEC - cnpLINKer
Dimensions
EBSCO (relevant databases)
EBSCO Discovery Service
Genamics JournalSeek
Google Scholar
Japan Science and Technology Agency (JST)
J-Gate
Journal Citation Reports/Science Edition
JournalGuide
JournalTOCs
KESLI-NDSL (Korean National Discovery for Science Leaders)
Mathematical Reviews (MathSciNet)
MyScienceWork
Naver Academic
Naviga (Softweco)
Norwegian Register for Scientific Journals, Series and Publishers
Primo Central (ExLibris)
ProQuest (relevant databases)
Publons
QOAM (Quality Open Access Market)
ReadCube
Scilit
SCImago (SJR)
SCOPUS
Semantic Scholar
Sherpa/RoMEO
Summon (ProQuest)
TDNet
Ulrich's Periodicals Directory/ulrichsweb
WanFang Data
Web of Science - Science Citation Index Expanded
WorldCat (OCLC)
X-MOL
Yewno Discover
zbMATH Open

Supplementary Materials

Topics

Volume 23 Issue 4

October 2023

Publicly Available October 17, 2023

Frontmatter

Page range: i-iii

Download PDF

October 12, 2023

Exploring tropical differential equations

Ethan Cotterill, Cristhian Garay López, Johana Luviano

Page range: 437-460

Abstract

The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry , and show how it may be used to extract combinatorial information about the set of power series solutions to a given system of differential equations, both in the archimedean (complex analytic) and in the non-Archimedean (e.g., p -adic) setting. A third and subsidiary aim is to show how tropical differential algebraic geometry is a natural application of semiring theory, and in so doing, contribute to the valuative study of differential algebraic geometry. We use this formalism to extend the fundamental theorem of partial differential algebraic geometry to the differential fraction field of the ring of formal power series in arbitrarily (finitely many variables; in doing so we produce new examples of non-Krull valuations that merit further study in their own right.

October 17, 2023

On the bond polytope

Markus Chimani, Martina Juhnke-Kubitzke, Alexander Nover

Page range: 461-480

Abstract

While the maximum cut problem and its corresponding polytope has received a lot of attention inliterature, comparably little is known about the natural closely related variant maximum bond. Here, given a graph G = (V, E) , we ask for a maximum cut δ(S) ⊆ E with S ⊆ V under the restriction that both G [ S ] as well as G [ V \ S ] are connected. Observe that both the maximum cut and the maximum bond can be seen as inverse problems to the traditional minimum cut, as there, the connectivity arises naturally in optimal solutions. The bond polytope is the convex hull of all incidence vectors of bonds. Similar to the connection of the corresponding optimization problems, the bond polytope is closely related to the cut polytope. While the latter has been intensively studied, there are no results on bond polytopes. We start a structural study of the latter, which additionally allows us to deduce algorithmic consequences. We investigate the relation between cut- and bond polytopes and the additional intricacies that arise when requiring connectivity in the solutions. We study the effect of graph modifications on bond polytopes and their facets, akin to what has been spearheaded for cut polytopes by Barahona, Grötschel and Mahjoub [4; 3] and Deza and Laurant [17; 15; 16]. Moreover, we study facet-defining inequalities arising from edges and cycles for bond polytopes. In particular, these yield a complete linear description of bond polytopes of cycles and 3-connected planar ( K 5 − e )-minor free graphs. Finally, we present a reduction of the maximum bond problem on arbitrary graphs to the maximum bond problem on 3-connected graphs. This yields a linear time algorithm for maximum bond on ( K 5 − e )-minor free graphs.

Open Access October 13, 2023

Universal convex covering problems under translations and discrete rotations

Mook Kwon Jung, Sang Duk Yoon, Hee-Kap Ahn, Takeshi Tokuyama

Page range: 481-500

More Download PDF

Abstract

We consider the smallest-area universal covering of planar objects of perimeter 2 (or equivalently, closed curves of length 2) allowing translations and discrete rotations. In particular, we show that the solution is an equilateral triangle of height 1 when translations and discrete rotations of π are allowed. We also give convex coverings of closed curves of length 2 under translations and discrete rotations of multiples of π /2 and of 2 π /3. We show that no proper closed subset of that covering is a covering for discrete rotations of multiples of π /2, which is an equilateral triangle of height smaller than 1, and conjecture that such a covering is the smallest-area convex covering. Finally, we give the smallest-area convex coverings of all unit segments under translations and discrete rotations of 2 π / k for all integers k =3.

October 14, 2023

Ehrhart theory of paving and panhandle matroids

Derek Hanely, Jeremy L. Martin, Daniel McGinnis, Dane Miyata, George D. Nasr, Andrés R. Vindas-Meléndez, Mei Yin

Page range: 501-526

Abstract

We show that the base polytope P M of any paving matroid M can be systematically obtained from a hypersimplex by slicing off certain subpolytopes, namely base polytopes of lattice path matroids corresponding to panhandle-shaped Ferrers diagrams. We calculate the Ehrhart polynomials of these matroids and consequently write down the Ehrhart polynomial of P M , starting with Katzman’s formula for the Ehrhart polynomial of a hypersimplex. The method builds on and generalizes Ferroni’s work on sparse paving matroids. Combinatorially, our construction corresponds to constructing a uniform matroid from a paving matroid by iterating the operation of stressed-hyperplane relaxation introduced by Ferroni, Nasr and Vecchi, which generalizes the standard matroid-theoretic notion of circuit-hyperplane relaxation. We present evidence that panhandle matroids are Ehrhart positive and describe a conjectured combinatorial formula involving chain forests and Eulerian numbers from which Ehrhart positivity of panhandle matroids will follow. As an application of the main result, we calculate the Ehrhart polynomials of matroids associated with Steiner systems and finite projective planes, and show that they depend only on their design-theoretic parameters: for example, while projective planes of the same order need not have isomorphic matroids, their base polytopes must be Ehrhart equivalent.

October 11, 2023

A partial compactification of the Bridgeland stability manifold

Barbara Bolognese

Page range: 527-541

Abstract

Bridgeland stability manifolds of Calabi–Yau categories are of noticeable interest both in mathematics and physics. By looking at some of the known examples, a pattern clearly emerges and gives a fairly precise description of how they look like. In particular, they all seem to have missing loci, which tend to correspond to degenerate stability conditions vanishing on spherical objects. Describing such missing strata is also interesting from a mirror-symmetric perspective, as they conjecturally parametrize interesting types of degenerations of complex structures. All the naive attempts at constructing modular partial compactifications show how elusive and subtle the problem in fact is: ideally, the missing strata would correspond to stability manifolds of quotient triangulated categories, but establishing such a correspondence on the geometric level and viewing stability conditions on quotients of the original triangulated category as suitable degenerations of stability conditions is not straightforward. In this paper, we will present a method to construct such partial compactifications if some additional hypotheses are satisfied, by realizing our space of interest as a suitable metric completion of the stability manifold.

October 17, 2023

The geometry of discrete L-algebras

Wolfgang Rump

Page range: 543-565

Abstract

The relationship of discrete L -algebras to projective geometry is deepened and made explicit in several ways. Firstly, a geometric lattice is associated to any discrete L -algebra. Monoids of I-type are obtained as a special case where the perspectivity relation is trivial. Secondly, the structure group of a non-degenerate discrete L -algebra X is determined and shown to be a complete invariant. It is proved that X ∖ {1} is a projective space with an orthogonality relation. A new definition of non-symmetric quantum sets, extending the recursive definition of symmetric quantum sets, is provided and shown to be equivalent to the former one. Quantum sets are characterized as complete projective spaces with an anisotropic duality, and they are also characterized in terms of their complete lattice of closed subspaces, which is one-sided orthomodular and semimodular. For quantum sets of finite cardinality n > 3, a representation as a projective space with duality over a skew-field is given. Quantum sets of cardinality 2 are classified, and the structure group of their associated L -algebra is determined.

October 17, 2023

Projective self-dual polygons in higher dimensions

Ana Chavez-Caliz

Page range: 567-582

Abstract

This paper examines the moduli space M m , n , k of m -self-dual n -gons in ℙ k . We present an explicit construction of self-dual polygons and determine the dimension of M m , n , k for certain n and m . Additionally, we propose a conjecture that extends Clebsch’s theorem, which states that every pentagon in ℝℙ 2 is invariant under the Pentagram map.

Volume 23 (2023)

Volume 22 (2022)

Volume 21 (2021)

Volume 20 (2020)

Volume 19 (2019)

Volume 18 (2018)

Volume 17 (2017)

Volume 16 (2016)

Volume 15 (2015)

Volume 14 (2014)

Volume 13 (2013)

Volume 12 (2012)

Volume 11 (2011)

Volume 10 (2010)

Volume 9 (2009)

Volume 8 (2008)

Volume 7 (2007)

Volume 6 (2006)

Volume 5 (2005)

Volume 4 (2004)

Volume 3 (2003)

Volume 2 (2002)

Volume 1 (2001)

Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
5-year Journal Impact Factor	0.5	2022, Journal Citation Reports (Clarivate, 2023)
Journal Citation Indicator	0.52	2022, Journal Citation Reports (Clarivate, 2023)
CiteScore	1.0	2022, Scopus (Elsevier B.V., 2023)
SCImago Journal Rank	0.393	2022, SJR (Scimago Lab, 2023; Data Source: Scopus)
Source Normalized Impact per Paper	0.839	2022, CWTS Journal Indicators (CWTS B.V., 2023; Data Source: Scopus)
Mathematical Citation Quotient	0.61

More information about journal rankings

Submit

Submission
Manuscript submission is done electronically by emailing a single PDF file (do not send any source files at this stage) to advgeom@mathematik.uni-wuerzburg.de.

Your benefits of publishing with us

Rapid online publication ahead-of-print with short turnaround times
Optional open access publication
Accepted papers will be published online first as DOI-citable, forward-linked articles for quickest possible visibility for the scientific community
Every article easily discoverable through SEO and comprehensive abstracting and indexing services
Secure archiving by De Gruyter and the independent archiving service Portico
Professional sales and marketing activities

Submission process

Submission of your paper by e-mail
Peer review process
Decision on your paper
If accepted: you have the option to publish it open access
Publication online and in print

Please note

Manuscripts must be written in clear and concise English
Before submitting your article please have a look at Ethical Guidelines and our Copyright Transfer Agreement
Once your article is accepted you have the option to publish it open access
Our Repository Policy allows you to distribute 30 PDF copies of your published article to colleagues (the PDF has to include the information that it is an author's copy). Please also feel free to distribute the link to the online abstract
If you have any general questions please visit our FAQ page for authors

We look forward to receiving your manuscript!

Hybrid Open Access

In this journal, authors have the option to publish their article under an open access license. Open Access allows you as an author to retain copyright and share your findings with colleagues and interested parties worldwide without any restraints.
Please note that authors from institutions with which we have a transformative agreement can publish open access without paying an article processing charge (APC). More information on the eligible institutions and articles can be found under the "Funding and Support" tab here.

Editorial

Managing Editors

Theo Grundhöfer
Institut für Mathematik
Universität Würzburg
Emil-Fischer-Str. 30
97074 Würzburg, Germany
E-mail: advgeom@mathematik.uni-wuerzburg.de

Michael Joswig
Institut für Mathematik
Technische Universität Berlin
Sekretariat MA 6-2
Straße des 17. Juni 136
10623 Berlin, Germany

Editors

John Bamberg
Centre for the Mathematics of Symmetry and Computation
The University of Western Australia (M019)
35 Stirling Highway
Crawley, WA 6009, Australia

Eiichi Bannai
Faculty of Mathematics
Kyushu University
744, Motooka, Nishi-ku,
Fukuoka, Japan 819-0395

Renzo Cavalieri
Department of Mathematics
Colorado State University
Fort Collins, CO 80523-1874, USA

Izzet Coskun
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL 60607, USA

Hans Cuypers
Department of Mathematics and Computer Science
Eindhoven University of Technology
5600 MB Eindhoven, Netherlands

Patrick Eberlein
Department of Mathematics
University of North Carolina
CB 3250 Phillips Hall
Chapel Hill, NC 27599-3250, USA

Graziano Gentili
Dipartimento di Matematica
Universitá degli Studi di Firenze
Viale Morgagni, 67/a
50134 Firenze, Italy

Martin Henk
Institut für Mathematik
Technische Universität Berlin
Sekretariat MA 4-1
Straße des 17. Juni 136
10623 Berlin, Germany

Milena Hering
School of Mathematics
University of Edinburgh
Edinburgh EH9 3JZ, United Kingdom

William M. Kantor
Department of Mathematics
University of Oregon
Eugene, OR 97403-1222, USA

Gábor Korchmáros
Dipartimento di Matematica
Università degli Studi della Basilicata
Via Nazario Sauro 85
85100 Potenza, Italy

Alexander Kreuzer
Fachbereich Mathematik
Universität Hamburg
Bundesstr. 55
20146 Hamburg, Germany

Jeffrey C. Lagarias
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, Michigan 48109-1043, USA

Thomas Leistner
School of Mathematical Sciences
The University of Adelaide
Adelaide SA 5005, Australia

Rainer Löwen
Institut fur Analysis/Topologie
TU Braunschweig
Pockelsstr. 14
38106 Braunschweig, Germany

Kaoru Ono
Research Institute for Mathematical Sciences
Kyoto University
Kyoto, 606-8502 Japan

Daniel Plaumann
Fakultät für Mathematik
Technische Universität Dortmund
Vogelpothsweg 87
44227 Dortmund, Germany

Francisco Santos
Departamento de Matemáticas, Estadística y Computación
Universidad de Cantabria
Av. de los Castros 48
39005 Santander, Spain

Steven H. Weintraub
Department of Mathematics
Lehigh University
Bethlehem, PA 18015-3174, USA

Richard Weiss
Department of Mathematics
Tufts University
503 Boston Avenue
Medford, MA 02155, USA

Technical Editor

Nils Rosehr
Institut für Mathematik
Universität Würzburg
Emil-Fischer-Str. 30
97074 Würzburg, Germany

(Deutsch)

Online ISSN: 1615-7168
Print ISSN: 1615-715X
Type: Journal
Language: English
Publisher: De Gruyter
First published: March 1, 2001
Publication Frequency: 4 Issues per Year
Audience: Researchers in the field of geometry